Biting kitten as night when sleeping

I have an 8-9 week old kitten. She has been the perfect animal except
for one bad habit. When I am sleeping, usually 3-4am in the morning,
she will curl up next to my head on the pillow or on my chest. She
will then stretch her paws and put them on my face and start taking
small bites or nips at my chin or anywhere I let her near my face.
She always wakes me up and I spend the next hour trying to get her to
stop.

She's not being aggressive and is usually purring. She is very
persistent. The only thing which helps, sometimes, is by placing my
finger in her mouth when she bites and saying no.

What is this behavior? Will she grow out of it? Has anyone else had
this problem and how did you handle it?

thanks